Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

One particle has a charge of [tex]-1.87 \times 10^{-9} \, C[/tex], while another particle has a charge of [tex]-1.10 \times 10^{-9} \, C[/tex]. If the two particles are separated by 0.05 m, what is the electromagnetic force between them?

The equation for Coulomb's law is [tex]F_e = \frac{k q_1 q_2}{r^2}[/tex], and the constant, [tex]k[/tex], equals [tex]9.00 \times 10^9 \, N \cdot m^2 / C^2[/tex].

A. [tex]-7.41 \times 10^{-6} \, N[/tex]
B. [tex]-3.70 \times 10^{-7} \, N[/tex]
C. [tex]7.41 \times 10^{-6} \, N[/tex]
D. [tex]3.70 \times 10^{-7} \, N[/tex]

Sagot :

GinnyAnswer
To find the electromagnetic force between the two particles, we'll use Coulomb's law, which is given by the formula:

[tex]\[ F_e = \frac{k q_1 q_2}{r^2} \][/tex]

where:
- [tex]\(k\)[/tex] is Coulomb's constant, [tex]\(9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2\)[/tex],
- [tex]\(q_1\)[/tex] and [tex]\(q_2\)[/tex] are the charges of the particles,
- [tex]\(r\)[/tex] is the separation distance between the charges.

Given data:
- [tex]\( q_1 = -1.87 \times 10^{-9} \, \text{C} \)[/tex]
- [tex]\( q_2 = -1.10 \times 10^{-9} \, \text{C} \)[/tex]
- [tex]\( r = 0.05 \, \text{m} \)[/tex]

Now substitute these values into the formula:

[tex]\[ F_e = \frac{(9.00 \times 10^9) \times (-1.87 \times 10^{-9}) \times (-1.10 \times 10^{-9})}{(0.05)^2} \][/tex]

First, calculate the numerator:

[tex]\[ (9.00 \times 10^9) \times (-1.87 \times 10^{-9}) \times (-1.10 \times 10^{-9}) \][/tex]

The product of the charges ([tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex]) will be positive because multiplying two negative numbers yields a positive result. Simplifying this, we get:

[tex]\[ (9.00 \times 10^9) \times (1.87 \times 10^{-9}) \times (1.10 \times 10^{-9}) = 9.00 \times 1.87 \times 1.10 \times 10^9 \times 10^{-9} \times 10^{-9} \][/tex]

[tex]\[ = 9.00 \times 1.87 \times 1.10 \times 10^{-9} \][/tex]

Next, calculate the denominator:

[tex]\[ (0.05)^2 = 0.0025 \][/tex]

Now substitute these into the expression for [tex]\( F_e \)[/tex]:

[tex]\[ F_e = \frac{9.00 \times 1.87 \times 1.10 \times 10^{-9}}{0.0025} \][/tex]

Calculate the values:

[tex]\[ 9.00 \times 1.87 = 16.83 \][/tex]

[tex]\[ 16.83 \times 1.10 = 18.513 \][/tex]

[tex]\[ F_e = \frac{18.513 \times 10^{-9}}{0.0025} \][/tex]

[tex]\[ F_e = 18.513 \times 10^{-9} \times \frac{1}{0.0025} \][/tex]

[tex]\[ F_e = 18.513 \times 10^{-9} \times 400 \][/tex]

[tex]\[ F_e = 7.4052 \times 10^{-6} \, \text{N} \][/tex]

Therefore, the electromagnetic force between the two particles is:

[tex]\[ \boxed{7.41 \times 10^{-6} \, \text{N}} \][/tex]

So the correct answer is:

C) [tex]\(7.41 \times 10^{-6} \, \text{N}\)[/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.